Such a method and such an apparatus are known from U.S. Pat. No. 6,190,913 B1. This known technique employs a pre-sterilized flexible plastic bag in which cells are cultivated. The bag is partially filled with growth media and the remainder of the bag is continuously purged with air or other oxygen-rich gas. The bag is secured to a rocking platform that is rocked to and fro about one horizontal axis by the alternate actuation of pneumatic pistons. The rocking motion promotes wave formation in the bag which provides liquid mixing and enhances oxygen transfer from the headspace gas to the liquid phase where it is essential for cell growth and metabolism. Adequate gas-liquid mass transfer (oxygen supply and carbon dioxide removal) is one of the important parameters for bioreactor design and functioning, and also plays a decisive role in strategies for upscaling culturing systems (see Dhanasekharan, K., BioProcess Int., March 2006, pages 2-6).